Can Conservation Laws be Derived from Symmetry and Newton's Laws?

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SUMMARY

This discussion centers on the derivation of conservation laws, specifically momentum and energy, from Newton's Laws through the principles of symmetry. It references the work of John Baez on Noether's theorem, which connects symmetries to conservation laws. The conversation highlights that while Newton's framework does not explicitly define energy conservation, it is essential to consider variational principles to fully understand these concepts, especially in the context of frictional systems.

PREREQUISITES
  • Newton's Laws of Motion
  • Noether's Theorem
  • Variational Principles in Physics
  • Understanding of Energy Conservation Concepts
NEXT STEPS
  • Study Noether's Theorem and its implications on conservation laws
  • Explore variational principles in classical mechanics
  • Investigate the relationship between symmetry and conservation laws in physics
  • Analyze case studies of frictional systems and energy conservation
USEFUL FOR

Physicists, students of classical mechanics, and anyone interested in the foundational principles of conservation laws and their derivations from symmetry.

xboy
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Is it possible to show directly from Newton's Laws that conservation of momentum and energy follow from principles of symmetry?
 
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xboy said:
Is it possible to show directly from Newton's Laws that conservation of momentum and energy follow from principles of symmetry?

I think you also need to postulate that there is some variational principle. After all, frictional systems can be time invariant, and nevertheless, there is no conservation of energy.
 

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